Non-linear Information Inequalities

Abstract

We construct non-linear information inequalities from Mat´uˇs’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they are the first non-trivial examples of non-linear information inequalities.

Keywords

• Entropy
• entropy function
• nonlinear information inequality
• nonshannon type information inequality